Question

2sin квадрат x+6= 13sin2x помогите срочно

Answer 1

$2sin^2x+6=13sin2x \\ 2sin^2x+6=26sinxcosx(:cos^2x) \\ 2tg^2x+6+6tg^2x=26tgx \\ 8tg^2x-20tgx+6=0(:2) \\ 4tg^2x-10tgx+3=0 \\ D=100-48=52=2 \sqrt{13} \\ tgx_1= \frac{10-2 \sqrt{13} }{8}(:2)= \frac{5- \sqrt{13} }{4} \\ tgx_2= \frac{5+ \sqrt{13} }{4} \\ \\ x_1= arctg(\frac{5- \sqrt{13} }{4})+ \pi k \\ x_2=arctg(\frac{5+ \sqrt{13} }{4}) + \pi k$